ALGEBRAIC PROPERTIES OF TOEPLITZ OPERATORS WITH SEPARATELY QUASIHOMOGENEOUS SYMBOLS ON THE BERGMAN SPACE OF THE UNIT BALL

In this paper we discuss some algebraic properties of Toeplitz operators with separately quasihomogeneous symbols (i.e., symbols being of the form ξkφ(|z1|,...,|zn|)) on the Bergman space of the unit ball in ℂn. We provide a decomposition of L2(Bn,dv), then we use it to show that the zero product of...

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Bibliographic Details
Published in:Journal of operator theory 2011-06, Vol.66 (1), p.193-207
Main Authors: DONG, XING-TANG, ZHOU, ZE-HUA
Format: Article
Language:English
Subjects:
Algebra
Analytic functions
Commuting
Differential equations
Marital property
Mathematical functions
Mathematical theorems
Operator theory
Unit ball
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Summary:In this paper we discuss some algebraic properties of Toeplitz operators with separately quasihomogeneous symbols (i.e., symbols being of the form ξkφ(|z1|,...,|zn|)) on the Bergman space of the unit ball in ℂn. We provide a decomposition of L2(Bn,dv), then we use it to show that the zero product of two Toeplitz operators has only a trivial solution if one of the symbols is separately quasihomogeneous and the other is arbitrary. Also, we describe the commutant of a Toeplitz operator whose symbol is radial.
ISSN:0379-4024
1841-7744